It isn't necessary to use Exif to embed arbitrary data inside an image. Could as well use PNG extra chunk, JFIF app marker, or simply append data to the end of the file.

It would be more interesting to devise a method that survives all extra data stripping and re-encoding, perhaps taking advantage of deterministic encoders, assuming they don't randomize pixel data on purpose.

In other words: turning the image data stream itself into a polyglot.